Limits at infinity
Milestone 5
by:Nancy-mirna-sama-yo
ussef diaa
Rule.
1- when the upper degree greater than the lower degree we use x m-n.
2- when lower degree greater than the upper degree y=0
3- when the lower degree and the upper degree areequal we use leading coefficient
Leading coefficient
Q1:for the rational functions f(x)=p(x)/q(x),q(x)≠0,p(x) and q(x) polynomial
functions, find algebrically the horizontal asymptotes, if they exist, by
finding the limits of the functions as x ∞.
a. y= -2x+3
X+1
b. X+2
-3x 2 +3x-1
x2 +25
d. y=3x+2
x2-1
x 3 -2 = x
=-2/1
H.A=-2
c. x 3 -25
H.A=0
H.A= ∞
H.A=0
e.y= x3 +x-4
4x3 +3x2 +x
=¼
f. X2 +1
x-1
g. X2 +3x
x5-1
=X2-1
h. x5 -2x
x 3 -x+1
= x5-3
=X2
H.A=¼
H.A=∞
H.A=0
H.A=∞
Q2: summarize your findings in question one in a table.
Degree
(p(x))
Leading
coefficient
Degree
Leading
coefficient
Horizontal
asymptote
a
1
-2
1
1
y=-2
b
-1
1
2
-3
y=0
c
3
1
2
1
y=x1
d
1
3
2
1
y=0
e
3
1
3
4
y=1/4
f
2
1
1
1
y=x1
g
2
3
5
1
y=0
h
5
1
3
1
y=x1